Impact Crater Detection on Mars Digital Elevation and Image Model

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1 Impact Crater Detection on Mars Digital Elevation and Image Model Mert Değirmenci Department of Computer Engineering, Middle East Technical University, Turkey Shatlyk Ashyralyyev Department of Computer Engineering, Middle East Technical University, Turkey

2 Outline - Problem Definition - Overview of the Algorithm - Crater Detection - Scale Invariant Feature Transform - Multi Population Genetic Algorithm - Basin Detection - Drainage Network Extraction - Crater Verification - Experiments & Results

3 Problem Definition - The extraction of Martian impact craters. - Two different datasets. ( Optical, Elevation ) (A) (B) Figure 1 : (A) Image acquired from Mars Digital Image Mosaic (B) from Mars Orbital Laser Altimeter, both acquisited on 0.15 West, 9.36 North, East, South.

4 Overview of the Algorithm Figure 2: Architecture of the System developed.

5 Crater Detection - Crater rims are repsented as ellipses. - Ellipse representation is problematic. - Degradation of craters due to erosional processes. - Two staged of solution : - SIFT + Edge point detection - Multi-Population Genetic Algorithm

6 Scale Invariant Feature Transform - Proposed by Lowe [1]. - Transform into collection of feature vectors that are invariant to - Scaling, rotation & Illumination changes. - Good localization on crater rims : Figure 3: (A) Optical data obtained from Mars surface (B) SIFT features highlighted (C) Edges extracted by canny edge detector

7 Ellipse Detection Algorithms - Literature of Martian Impact Crater Detectors use Hough Transform based methods. - Hough Transformation (HT) : - Image space to parameter space - Parameter space grows exponentially along with number of parameters. - Appropriate for simple primitives such as lines. - Huge complexity for ellipse detection.

8 Ellipse Detection Algorithms - Randomized Hough Transform (RHT) : - A solution to the complexity problem of HT. - Randomly sample a number of points. - Calculate subset of parameter space. - Randomness can be traded with Accuracy. - A blind search on parameter space. - No feedback information from the ellipses.

9 Ellipse Detection Algorithms - Genetic Algorithm (GA) : - Solution to the problems associated with RHT. - Evolve solutions using the feedback of their fitness. - Find an approximate solution to the optimization problems. - Sketch of the Algorithm - Until Convergence - Evolve the solutions to find fittest one. - Evolution : Mutation & Crossover. - Globally optimal ellipse? - We prefer multiple locally optimal ellipses.

10 Ellipse Detection Algorithms - Generalize GA to find multiple local optimas. - Sharing Genetic Algorithm (SGA) : - Fitness of similar individuals is shared. - Search is guided towards uninhabitat areas. - Locally optimal ellipses are promoted. - Multi-Population Genetic Algorithm (MPGA) : - A number of islands that can communicate. - Better performance on ellipse detection [2].

11 Multi-Population Genetic Algorithm - Multiple populations promote local optima search. - Sketch of the algorithm. - Evolve a number of solutions (ellipses ). - Each solution lives on closest island. - No island close enough? - An individual (ellipse) can create her own island. - Input : SIFT features + Edges - Output : Ellipses

12 Multi-Population Genetic Algorithm - An iteration of MPGA : Figure 4: One iteration of Multi-Poulation Genetic Algorithm

Multi-Population Genetic Algorithm - How to represent an individual solution? - Directly by parameters of ellipse [3] - Search towards non-existent ellipses.

13 Multi-Population Genetic Algorithm - How to represent an individual solution? - Directly by parameters of ellipse [3] - Search towards non-existent ellipses. - The minimal number of points that are able to characterize an ellipse [2]. - Five keypoints are enough. Figure 5: An individual which represents an ellipse determined by five SIFT keypoints.

14 Multi-Population Genetic Algorithm - How to evaluate the fitness of an individual. - Match the template of ellipse around edges [2]. - For Martian impact crater detection : Edges do not clearly distinguish craters. - In our implementation SIFT features are also used when template is matched around the solution. - Weigh of an edge response is lower than a SIFT feature.

15 Multi-Population Genetic Algorithm - Merging of Subpopulations : - Necessary to prevent replication. - How to measure distance between populations? - Measure the distance between individuals. - How to merge populations. - Take the first half of the fittest individuals. - The number of individuals are decreased. - Produce random individuals to protect the balance.

16 Multi-Population Genetic Algorithm - Each individual lives on matching island. - Migraiton : - Choose the closest population. - Splitting : - Create new population when no population is close. - Evolution : finding the fittest individuals. - Crossover : - Mate the individuals, produce offspings, keep fittest. - Mutation : - Randomly change the chromosome of the individual. - Low priority. - Inspired by evolutionary biology.

17 Multi-Population Genetic Algorithm - Uniform crossover is implemented which exchanges the points determining ellipses (individuals). Figure 6: Uniform crossover operation over two individuals P1 and P2 which produces the offspring O1

18 Basin Detection - Need to determine the locations of basins to verify craters extracted. - The drainage networks must be extracted from digital elevation data. - Two solutions : - Hydrological approaches. - Depends on flow accumulation. - Morphological approaches. - Depends on shape of the basins.

19 Basin Detection - Hydrological approach is chosen since impact craters are topographic basins. - When subject to enough rain, they become lakes. - Two well-known hydrological approach : - Deterministic 8 (D8) [4] - Simulate the water on each cell flowing through lower elevation of highest slope in adjacent eight cells. - What happens on planar areas? - Divergent flow.

20 Basin Detection - Multiple flow direction model (MFDM) [5] : - Water in each cell flows through all lower elevation cells. - The distribution of the water is given by : - Where Si is the slope of the adjacent cell, and w is the exponent determining weight.

21 Basin Detection - We have adapted MFDM on Mars Digital elevation data (MDEM) : Figure 7: Sink source detection on Mars Digital Elevation Model

22 Crater Verification - Need to merge the two result set : - Ellipses extracted from MDIM & MDEM - Basins extracted from MDEM. - The ratio of the area of basins under ellipses and the area of ellipse is thresholded. - Need to exclude duplicates. - The overlapping area of each pair of ellipses are compared to the area of the biggest one.

23 Experiments & Results - Input Data : Digital Elevation and Image - Available at NASA Web Map Server Test Site - Heavily Cratered. - Craters are degraded. - Bounding Box : 7.42, , , -7.58

24 Experiments & Results - The Metrics used for assessing quality. - Proposed by [6] - TP : True Positives - FP : False Positives - FN : False Negatives

25 Experiments & Results - Results for current algorithms : - Kim uses test sites that do not involve deformed craters. - Barlow Catalog is manually prepared.

26 Experiments & Results - Results for the algorithm we have proposed: - Detection = 73% - Close to best performing Algorithm. - Branching = Best Branching Factor in the literature. - Quality = 61% - Close to best performing Algorithm.

27 Conclusion & Future Work - Developed Flexible & Robust algorithm. - Flexible : Fitness function of MPGA can be improved. - Robust : Experiments have shown improvements. - Future Work : - Curvature values could be incorporated into fitness evaluation of a crater. Figure 8: Craters detected around famous Herschel crater.

28 References [Low99] D. G. Lowe, Object Detection from local scale-invariant features, Proceedings of the International Conference on Computer Vision, pp , [Yao05] J. Yao, N. Kharma, P. Grogono, A multipopulation genetic algorithm for robust and fast ellipse detection, Pattern Analysis & Applications, vol. 8 pp , [Man02] T. Mainzer, Genetic algorithm for shape detection, Technical report no. DCSE/TR , University of West Bohemia, [Cal84] J. F. O Callagnan, D. M. Mark, The extraction of drainage networks from digital elevation data, Comput. Vis. Graph. Image Process., vol. 28, no. 3, pp , Dec [Fre91] T.G. Freeman, Calculating catchment area with divergent flow based on a regular grid, Computer and Geoscience, pp , [Shu99] J. A. Shufelt, Performance evaluation and analysis of monocular building extraction from aerial imagery, IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 4, pp , [Bar88] N. G. Barlow, Crater size-distributions and a revised Martian relative chronology, Icarus, vol. 75, no. 2, pp , [Bue07] B. D. Bue, T. F. Stepinski Machine Detection of Martian Impact Craters From Digital Topography Data, IEEE Transactions on Geoscience and Remote Sensing, Vol.45, pp , 2007.

29 Thank you for your attention. Any questions?

Complex Geometric Primitive Extraction on Graphics Processing Unit

Complex Geometric Primitive Extraction on Graphics Processing Unit Mert Değirmenci Department of Computer Engineering, Middle East Technical University, Turkey mert.degirmenci@ceng.metu.edu.tr ABSTRACT